manifold is a topological space that locally resembles Euclidean space near each point. More precisely, an n {\displaystyle n} -dimensional manifold,...

In mathematics, a differentiable manifold (also differential manifold) is a type of manifold that is locally similar enough to a vector space to allow...

differential geometry, a Calabi–Yau manifold, also known as a Calabi–Yau space, is a particular type of manifold which has certain properties, such as...

geometry. Manifold may also refer to: Manifold (comics), a fictional character in Marvel Comics publications Manifold Records, a record label Manifold Trilogy...

In differential geometry, a Riemannian manifold (or Riemann space) is a geometric space on which many geometric notions such as distance, angles, length...

In mathematics, an algebraic manifold is an algebraic variety which is also a manifold. As such, algebraic manifolds are a generalisation of the concept...

In mathematics, a 4-manifold is a 4-dimensional topological manifold. A smooth 4-manifold is a 4-manifold with a smooth structure. In dimension four,...

In differential geometry, a symplectic manifold is a smooth manifold, M {\displaystyle M} , equipped with a closed nondegenerate differential 2-form,...

Albert Manifold (born 1962) is an Irish business executive, who was the chief executive officer of CRH plc from January 2014 to 2024, and then the chairman...

The manifold hypothesis posits that many high-dimensional data sets that occur in the real world actually lie along low-dimensional latent manifolds inside...

topology, a topological manifold is a topological space that locally resembles real n-dimensional Euclidean space. Topological manifolds are an important class...

mathematical physics, a pseudo-Riemannian manifold, also called a semi-Riemannian manifold, is a differentiable manifold with a metric tensor that is everywhere...

In geometry, a tame manifold is a manifold with a well-behaved compactification. More precisely, a manifold M {\displaystyle M} is called tame if it is...

Fedosov manifold is a symplectic manifold with a compatible torsion-free connection, that is, a triple (M, ω, ∇), where (M, ω) is a symplectic manifold (that...

collapsed manifold is an n-dimensional manifold M that admits a sequence of Riemannian metrics gi, such that as i goes to infinity the manifold is close...

Hadamard manifold, named after Jacques Hadamard — more often called a Cartan–Hadamard manifold, after Élie Cartan — is a Riemannian manifold ( M , g )...

In mathematics and especially differential geometry, a Kähler manifold is a manifold with three mutually compatible structures: a complex structure, a...

In mathematics, a 3-manifold is a topological space that locally looks like a three-dimensional Euclidean space. A 3-manifold can be thought of as a possible...

Poisson manifold is a smooth manifold endowed with a Poisson structure. The notion of Poisson manifold generalises that of symplectic manifold, which in...

differential geometry and complex geometry, a complex manifold or a complex analytic manifold is a manifold with a complex structure, that is an atlas of charts...

mathematics, a homology manifold (or generalized manifold) is a locally compact topological space X that looks locally like a topological manifold from the point...

Manifold, formerly known as Manifold Markets, is an online prediction market platform. Users engage in competitive forecasting using play money called...

geometry of smooth shapes and smooth spaces, otherwise known as smooth manifolds. It uses the techniques of vector calculus, linear algebra and multilinear...

mathematics, the slow manifold of an equilibrium point of a dynamical system occurs as the most common example of a center manifold. One of the main methods...

of a center manifold was originally developed to determine stability of degenerate equilibria. Subsequently, the concept of center manifolds was realised...

an Iwasawa manifold is a compact quotient of a 3-dimensional complex Heisenberg group by a cocompact, discrete subgroup. An Iwasawa manifold is a nilmanifold...

Manifold injection is a mixture formation system for internal combustion engines with external mixture formation. It is commonly used in engines with spark...

mathematics, inertial manifolds are concerned with the long term behavior of the solutions of dissipative dynamical systems. Inertial manifolds are finite-dimensional...

Manifold alignment is a class of machine learning algorithms that produce projections between sets of data, given that the original data sets lie on a...

An inlet manifold or intake manifold (in American English) is the part of an internal combustion engine that supplies the fuel/air mixture to the cylinders...

In mathematics, a Brieskorn manifold or Brieskorn–Phạm manifold, introduced by Egbert Brieskorn (1966, 1966b), is the intersection of a small sphere around...

almost complex manifold is a smooth manifold equipped with a smooth linear complex structure on each tangent space. Every complex manifold is an almost...

In differential geometry, a Sasakian manifold (named after Shigeo Sasaki) is a contact manifold ( M , θ ) {\displaystyle (M,\theta )} equipped with a special...

mathematics, in the theory of several complex variables and complex manifolds, a Stein manifold is a closed, complex submanifold of the vector space of n complex...

In mathematics, a Lefschetz manifold is a particular kind of symplectic manifold ( M 2 n , ω ) {\displaystyle (M^{2n},\omega )} , sharing a certain cohomological...

mathematics, a toric manifold is a topological analogue of toric variety in algebraic geometry. It is an even-dimensional manifold with an effective smooth...

space. Manifolds can be classified by increasing degree of this "resemblance" into topological manifolds, differentiable manifolds, smooth manifolds, and...

In topology, a branch of mathematics, a manifold M may be decomposed or split by writing M as a combination of smaller pieces. When doing so, one must...

Topological manifold Almost complex manifold Almost symplectic manifold Calibrated manifold Complex manifold Contact manifold CR manifold Finsler manifold Hermitian...

mathematics, dianalytic manifolds are possibly non-orientable generalizations of complex analytic manifolds. A dianalytic structure on a manifold is given by an...

digital manifold is a special kind of combinatorial manifold which is defined in digital space i.e. grid cell space. A combinatorial manifold is a kind...

the study of dynamical systems and differential equations, the stable manifold theorem is an important result about the structure of the set of orbits...

Synnot Manifold (30 March 1849 – 15 November 1928) was an Australian grazier and politician. Born in Melbourne, Manifold was the son of Thomas Manifold, the...

A manifold is a wider and/or larger pipe or channel, into which smaller pipes or channels lead, or a pipe fitting or similar device that connects multiple...

manifold learning, is any of various related techniques that aim to project high-dimensional data, potentially existing across non-linear manifolds (non-affine...

Manifold vacuum, or engine vacuum in a petrol engine is the difference in air pressure between the engine's intake manifold and Earth's atmosphere. Manifold...

In mathematics, the Wu manifold is a 5-manifold defined as a quotient space of Lie groups appearing in the mathematical area of Lie theory. Due to its...

In mathematics, a Haken manifold is a compact, P²-irreducible 3-manifold that is sufficiently large, meaning that it contains a properly embedded two-sided...

manifold, stable manifold, unstable manifold, subcenter manifold and inertial manifold. Typically, although by no means always, invariant manifolds are constructed...

In mathematics, a complete manifold (or geodesically complete manifold) M is a (pseudo-) Riemannian manifold for which, starting at any point p of M,...

Riemannian manifold. Ricci-flat manifolds are a special kind of Einstein manifold. In theoretical physics, Ricci-flat Lorentzian manifolds are of fundamental...

In differential geometry, in the category of differentiable manifolds, a fibered manifold is a surjective submersion π : E → B {\displaystyle \pi :E\to...

Manifold Garden is a puzzle video game developed by American artist William Chyr. It was released on Windows, macOS, and iOS on October 18, 2019. The player...

automotive engineering, an exhaust manifold collects the exhaust gases from multiple cylinders into one pipe. The word manifold comes from the Old English word...

The manifold absolute pressure sensor (MAP sensor) is one of the sensors used in an internal combustion engine's electronic control system. Engines that...

geometry, a Hermitian manifold is the complex analogue of a Riemannian manifold. More precisely, a Hermitian manifold is a complex manifold with a smoothly...

In mathematics, a differentiable manifold M {\displaystyle M} of dimension n is called parallelizable if there exist smooth vector fields { V 1 , … , V...

The Manifold Trilogy is a series of science fiction books by British author Stephen Baxter. The series was published from 1999 to 2003. It consists of...

define integrands over curves, surfaces, volumes, and higher-dimensional manifolds. The modern notion of differential forms was pioneered by Élie Cartan...

branch of differential geometry that studies Riemannian manifolds. An example of a Riemannian manifold is a surface, on which distances are measured by the...

Manifold Records is a US-based record label and mailorder store specializing in experimental, ambient and other hard-to-define audio materials. Begun in...

topology, a branch of mathematics, a Mazur manifold is a contractible, compact, smooth four-dimensional manifold-with-boundary which is not diffeomorphic...

In mathematics, an analytic manifold, also known as a C ω {\displaystyle C^{\omega }} manifold, is a differentiable manifold with analytic transition maps...

graded manifolds are extensions of the concept of manifolds based on ideas coming from supersymmetry and supercommutative algebra. Both graded manifolds and...

A hydraulic manifold is a component that regulates fluid flow between pumps and actuators and other components in a hydraulic system. It is like a switchboard...

A cylinder manifold is system of pipes and valves for using a group of gas cylinders, or boil-off from vacuum insulated evaporators, to feed a single supply...

In differential geometry, a hyperkähler manifold is a Riemannian manifold ( M , g ) {\displaystyle (M,g)} endowed with three integrable almost complex...

In geometry, if X is a manifold with an action of a topological group G by analytical diffeomorphisms, the notion of a (G, X)-structure on a topological...

In mathematics, a closed manifold is a manifold without boundary that is compact. In comparison, an open manifold is a manifold without boundary that has...

mathematics, contact geometry is the study of a geometric structure on smooth manifolds given by a hyperplane distribution in the tangent bundle satisfying a...

In complex geometry, a Hopf manifold (Hopf 1948) is obtained as a quotient of the complex vector space (with zero deleted) ( C n ∖ 0 ) {\displaystyle ({\mathbb...

as real vector spaces, Euclidean spaces, surfaces, and more generally manifolds that allows a consistent definition of "clockwise" and "anticlockwise"...

In mathematics, a P2-irreducible manifold is a 3-manifold that is irreducible and contains no 2-sided R P 2 {\displaystyle \mathbb {R} P^{2}} (real projective...

The Manifold Way is a shared-use path in Staffordshire, England. It is 8 miles (12.9 km) in length and runs from Hulme End in the north to Waterhouses...

that is also a differentiable manifold, such that group multiplication and taking inverses are both differentiable. A manifold is a space that locally resembles...

Manifold Heights is a residential suburb of Geelong. At the 2016 census, Manifold Heights had a population of 2,649. It was named after Manifolds' vineyards...

field of differential geometry, a Frobenius manifold, introduced by Dubrovin, is a flat Riemannian manifold with a certain compatible multiplicative structure...

In the subject of manifold theory in mathematics, if M {\displaystyle M} is a topological manifold with boundary, its double is obtained by gluing two...

A scuba manifold is a device incorporating one or more valves and one or more gas outlets with scuba regulator connections, used to connect two or more...

precisely in topology and differential geometry, a hyperbolic 3-manifold is a manifold of dimension 3 equipped with a hyperbolic metric, that is a Riemannian...

Eden Fesi, also known as Manifold, is a superhero appearing in American comic books published by Marvel Comics. Created by Jonathan Hickman and Stefano...

alternative for such situations. Orientable manifolds with a spinc structure are called spinc manifolds. C stands for the complex numbers, which are...

mathematics, a statistical manifold is a Riemannian manifold, each of whose points is a probability distribution. Statistical manifolds provide a setting for...

John Streeter Manifold AM (21 April 1915 – 19 April 1985) was an Australian poet and critic. He was born in Melbourne, into a well known Camperdown family...

The River Manifold is a river in Staffordshire, England. It is a tributary of the River Dove (which also flows through the Peak District, forming the boundary...

uses external mixture formation is called a manifold injection system. There exist two types of manifold injection systems: multi-point (or "port") and...

mathematics, particularly in differential geometry, an Osserman manifold is a Riemannian manifold in which the characteristic polynomial of the Jacobi operator...

Sir (Thomas) Chester Manifold KBE (13 May 1897 – 6 January 1979) was prominent member of the Victorian Racing community as a successful racehorse owner...

In mathematics, a spherical 3-manifold M is a 3-manifold of the form M = S 3 / Γ {\displaystyle M=S^{3}/\Gamma } where Γ {\displaystyle \Gamma } is a finite...

geometry, an affine manifold is a differentiable manifold equipped with a flat, torsion-free connection. Equivalently, it is a manifold that is (if connected)...

piecewise-differentiable manifolds are manifolds that have piecewise smooth transition maps between their local coordinate charts. These generalise the manifolds in DIFF...

Peter Manifold (1817–1885) was an English pastoralist and politician of western Victoria. Born in 1817 to William and Mary Manifold in Bromborough, Cheshire...

and topology, a formal manifold can mean one of a number of related concepts: In the sense of Dennis Sullivan, a formal manifold is one whose real homotopy...

In mathematics, a Dold manifold is one of the manifolds P ( m , n ) = ( S m × C P n ) / τ {\displaystyle P(m,n)=(S^{m}\times \mathbb {CP} ^{n})/\tau }...

Manifold System is a geographic information system (GIS) software package developed by Manifold Software Limited that runs on Microsoft Windows. Manifold...

Kähler–Einstein metric on a complex manifold is a Riemannian metric that is both a Kähler metric and an Einstein metric. A manifold is said to be Kähler–Einstein...

Riemann manifold may refer to: Riemann surface in complex analysis Riemannian manifold in Riemannian geometry Zariski–Riemann space consisting of valuations...

theory is a collection of techniques used to produce one finite-dimensional manifold from another in a 'controlled' way, introduced by John Milnor (1961). Milnor...

In differential geometry, a G2 manifold or Joyce manifold is a seven-dimensional Riemannian manifold with holonomy group contained in G2. The group G...

mathematics, a 5-manifold is a 5-dimensional topological manifold, possibly with a piecewise linear or smooth structure. Non-simply connected 5-manifolds are impossible...

hyperbolic 3-manifolds, respectively. In these dimensions, they are important because most manifolds can be made into a hyperbolic manifold by a homeomorphism...

Nehari manifold is a manifold of functions, whose definition is motivated by the work of Zeev Nehari (1960, 1961). It is a differentiable manifold associated...

studies manifolds, or more generally topological spaces, of four or fewer dimensions. Representative topics are the theory of 3-manifolds and 4-manifolds, knot...

In mathematics, a CR manifold, or Cauchy–Riemann manifold, is a differentiable manifold together with a geometric structure modeled on that of a real hypersurface...

used to describe a manifold. An atlas consists of individual charts that, roughly speaking, describe individual regions of the manifold. In general, the...

In mathematics, the tangent space of a manifold is a generalization of tangent lines to curves in two-dimensional space and tangent planes to surfaces...

classification of manifolds is a basic question, about which much is known, and many open questions about manifolds remain. Low-dimensional manifolds are classified...

manifold is a cusped hyperbolic 3-manifold of finite volume. It is non-orientable and has the smallest volume among non-compact hyperbolic manifolds,...

In Riemannian geometry, an isoparametric manifold is a type of (immersed) submanifold of Euclidean space whose normal bundle is flat and whose principal...

mathematics, a Riemannian manifold is said to be flat if its Riemann curvature tensor is everywhere zero. Intuitively, a flat manifold is one that "locally...

The Edward Manifold Stakes is a Victoria Racing Club Group 2 Thoroughbred horse race for three year old fillies at set weights run over a distance of 1600...

In mathematics, a Moishezon manifold M is a compact complex manifold such that the field of meromorphic functions on each component M has transcendence...

topological manifold can be calculated. A connected topological manifold is locally homeomorphic to Euclidean n-space, in which the number n is the manifold's dimension...

differential manifold, which is a topological manifold with some additional mathematical structure that allows for differential calculus on the manifold. If M...

Rizza manifold, named after Giovanni Battista Rizza, is an almost complex manifold also supporting a Finsler structure: this kind of manifold is also...

In physics, the term simplicial manifold commonly refers to one of several loosely defined objects, commonly appearing in the study of Regge calculus....

In machine learning, manifold regularization is a technique for using the shape of a dataset to constrain the functions that should be learned on that...

In mathematics, a quasitoric manifold is a topological analogue of the nonsingular projective toric variety of algebraic geometry. A smooth 2 n {\displaystyle...

usual axiom of a manifold to be a Hausdorff space. In general topology, this axiom is relaxed, and one studies non-Hausdorff manifolds: spaces locally...

manifold is the unique compact, simply connected topological 4-manifold with intersection form the E8 lattice. The E 8 {\displaystyle E_{8}} manifold...

sub-Riemannian manifold is a certain type of generalization of a Riemannian manifold. Roughly speaking, to measure distances in a sub-Riemannian manifold, you are...

topological manifolds, which was understood in various forms since the 1860s. In higher dimensions, the closed and connected topological manifolds do not have...

In mathematics, a branched manifold is a generalization of a differentiable manifold which may have singularities of very restricted type and admits a...

an essential manifold is a special type of closed manifold. The notion was first introduced explicitly by Mikhail Gromov. A closed manifold M is called...

A normally hyperbolic invariant manifold (NHIM) is a natural generalization of a hyperbolic fixed point and a hyperbolic set. The difference can be described...

SageManifolds (following the styling of SageMath) is an extension fully integrated into SageMath, to be used as a package for differential geometry and...

of a symplectic manifold. A third construction, also due to Floer, associates homology groups to closed three-dimensional manifolds using the Yang–Mills...

Manifold was a mathematical magazine published at the University of Warwick. It was established in 1968. Its philosophy was "It is possible to be serious...

nonlinear analysis, a Fréchet manifold is a topological space modeled on a Fréchet space in much the same way as a manifold is modeled on a Euclidean space...

theory on natural bundles over a world manifold. A world manifold is a four-dimensional orientable real smooth manifold. It is assumed to be a Hausdorff and...

The uniform distribution on a Stiefel manifold is a matrix-variate distribution that plays an important role in multivariate statistics. There one often...

In topology, a graph manifold (in German: Graphenmannigfaltigkeit) is a 3-manifold which is obtained by gluing some circle bundles. They were discovered...

geometry and mathematical physics, an Einstein manifold is a Riemannian or pseudo-Riemannian differentiable manifold whose Ricci tensor is proportional to the...

geometry and differential topology that studies symplectic manifolds; that is, differentiable manifolds equipped with a closed, nondegenerate 2-form. Symplectic...

A block and bleed manifold is a hydraulic manifold that combines one or more block/isolate valves, usually ball valves, and one or more bleed/vent valves...

theory enables one to analyze the topology of a manifold by studying differentiable functions on that manifold. According to the basic insights of Marston...

Chester Manifold may refer to: James Chester Manifold (1867–1918), member of the Australian Parliament Sir Thomas Chester Manifold (1897–1979), his son...

manifold M of dimension divisible by four. This invariant of a manifold has been studied in detail, starting with Rokhlin's theorem for 4-manifolds,...

of mathematics, a prime manifold is an n-manifold that cannot be expressed as a non-trivial connected sum of two n-manifolds. Non-trivial means that neither...

systems, the idea of stable and unstable sets or stable and unstable manifolds give a formal mathematical definition to the general notions embodied...

In mathematics, a Hilbert manifold is a manifold modeled on Hilbert spaces. Thus it is a separable Hausdorff space in which each point has a neighbourhood...

timeline of manifolds, one of the major geometric concepts of mathematics. For further background see history of manifolds and varieties. Manifolds in contemporary...

all of the tangent spaces for all points on a manifold, structured in a way that it forms a new manifold itself. Formally, in differential geometry, the...

functions and manifolds are named after John Forbes Nash, Jr., who proved (1952) that any compact smooth manifold admits a Nash manifold structure, i.e...

structure of a Lorentzian manifold describes the possible causal relationships between points in the manifold. Lorentzian manifolds can be classified according...

In mathematics, the Stiefel manifold V k ( R n ) {\displaystyle V_{k}(\mathbb {R} ^{n})} is the set of all orthonormal k-frames in R n . {\displaystyle...

In mathematics, a Banach manifold is a manifold modeled on Banach spaces. Thus it is a topological space in which each point has a neighbourhood homeomorphic...

Complex manifolds that can be holomorphic embedded into C n {\displaystyle \mathbb {C} ^{n}} are called Stein manifolds. Also Stein manifolds satisfy...

In topology, the Prüfer manifold or Prüfer surface is a 2-dimensional Hausdorff real analytic manifold that is not paracompact. It was introduced by Tibor...

In hyperbolic geometry, the Meyerhoff manifold is the arithmetic hyperbolic 3-manifold obtained by ( 5 , 1 ) {\displaystyle (5,1)} surgery on the figure-8...

manifolds. A manifold is a topological space that resembles Euclidean space near each point. More precisely, each point of an n-dimensional manifold has...

theory of smooth manifolds, a congruence is the set of integral curves defined by a nonvanishing vector field defined on the manifold. Congruences are...

intake manifold, cast iron exhaust manifold fuel system common-rail multi-point electronic sequential indirect fuel injection with four intake manifold-sited...

compact manifolds of the same dimension, set up using the concept of the boundary (French bord, giving cobordism) of a manifold. Two manifolds of the same...

mathematics, a Spin(7)-manifold is an eight-dimensional Riemannian manifold whose holonomy group is contained in Spin(7). Spin(7)-manifolds are Ricci-flat and...

In mathematics, a LeBrun manifold is a connected sum of copies of the complex projective plane, equipped with an explicit self-dual metric. Here, self-dual...

geometry, a density is a spatially varying quantity on a differentiable manifold that can be integrated in an intrinsic manner. Abstractly, a density is...

In mathematics, a nearly Kähler manifold is an almost Hermitian manifold M {\displaystyle M} , with almost complex structure J {\displaystyle J} , such...

manifolds of the Lefschetz fixed-point formula that relates a sum over the fixed points of a holomorphic vector field of a compact complex manifold to...

Manifold: Space is a science fiction book by British author Stephen Baxter, first published in the United Kingdom in 2000, then released in the United...

The Hantzsche–Wendt manifold, also known as the HW manifold or didicosm, is a compact, orientable, flat 3-manifold, first studied by Walter Hantzsche and...

Manifold: Time is a 1999 science fiction novel by Stephen Baxter. It is the first of Baxter's Manifold Trilogy (the others being Manifold: Space and Manifold:...

Calabi–Yau manifold is a compact Kähler manifold which is Ricci-flat; as a special case of Yau's verification of the Calabi conjecture, such manifolds are known...

surface, or more generally in a Riemannian manifold. The term also has meaning in any differentiable manifold with a connection. It is a generalization...

theory is viewed as the special case of dimension one of the theory of manifolds and algebraic varieties. Nevertheless, many questions remain specific...

Legislative Assembly. Manifold was born on 29 March 1809 in Bromborough, England. He was the son of William Manifold and Mary Manifold (née Barnes). He had...

differential geometry, a fibered manifold is surjective submersion of smooth manifolds Y → X. Locally trivial fibered manifolds are fiber bundles. Therefore...

{\displaystyle \mathbf {Gr} _{k}(V)} , also known as a Grassmann manifold, is a differentiable manifold that parameterizes the set of all k {\displaystyle k} -dimensional...

tangent space T p M {\displaystyle T_{p}M} of a Riemannian manifold (or pseudo-Riemannian manifold) M {\displaystyle M} to M {\displaystyle M} itself. The...

The Manifold Trust was created by Sir John Smith in 1962 to generate funds for conservation in the UK, particularly of buildings, and to support other...

mathematics, geometric topology is the study of manifolds and maps between them, particularly embeddings of one manifold into another. Geometric topology as an...

compact extra dimensions must be shaped like a Calabi–Yau manifold. A Calabi–Yau manifold is a special space which is typically taken to be six-dimensional...

geometry, the cut locus of a point p on a manifold is the closure of the set of all other points on the manifold that are connected to p by two or more distinct...

curvature is one of the ways to describe the curvature of Riemannian manifolds. The sectional curvature K ( σ p ) {\displaystyle K(\sigma _{p})} depends...

gives a tangent vector at each point of the manifold (that is, a section of the tangent bundle to the manifold). Vector fields are one kind of tensor field...

valve springs and intake manifold design. The “Street” engine featured a heated intake manifold, cast iron exhaust manifolds, automatic choke, and a milder...

In mathematics, the Whitehead manifold is an open 3-manifold that is contractible, but not homeomorphic to R 3 . {\displaystyle \mathbb {R} ^{3}.} It was...

Cavern and Thyrsis's Cave) is a natural cavern located at SK09865496 in the Manifold Valley of the White Peak in Staffordshire, England. It is classified as...

mathematics, particularly differential geometry, a Finsler manifold is a differentiable manifold M where a (possibly asymmetric) Minkowski norm F(x, −) is...

Gauss–Bonnet theorem (for 2-dimensional manifolds / surfaces) to higher even-dimensional Riemannian manifolds. In 1943, Carl B. Allendoerfer and André...

In differential geometry, a spin structure on an orientable Riemannian manifold (M, g) allows one to define associated spinor bundles, giving rise to the...

stochastic analysis on manifolds or stochastic differential geometry is the study of stochastic analysis over smooth manifolds. It is therefore a synthesis...

D. Hodge, is a method for studying the cohomology groups of a smooth manifold M using partial differential equations. The key observation is that, given...

on manifolds so one can define (differentiable) manifolds as a set isomorphic to a vector manifold. The difference lies in that a vector manifold is algebraically...

manifold or pseudo-Riemannian manifold that preserves the metric. Flows generated by Killing vector fields are continuous isometries of the manifold....

charge from each turbocharger into a single intake manifold, while others use a separate intake manifold for each turbocharger. Parallel configurations are...

22°41′S 150°50′E / 22.683°S 150.833°E / -22.683; 150.833 Cape Manifold (22°41′S 150°50′E / 22.683°S 150.833°E / -22.683; 150.833) is a coastal headland...

differential geometry, an almost symplectic structure on a differentiable manifold M {\displaystyle M} is a non-degenerate two-form ω {\displaystyle \omega...

the cotangent bundle of a smooth manifold is the vector bundle of all the cotangent spaces at every point in the manifold. It may be described also as the...

non-Jordan manifolds. A combinatorial manifold is a kind of manifold which is a discretization of a manifold. It usually means a piecewise linear manifold made...

differential geometry, a quaternion-Kähler manifold (or quaternionic Kähler manifold) is a Riemannian 4n-manifold whose Riemannian holonomy group is a subgroup...

non-paracompact manifolds in higher dimensions include the Prüfer manifold, products of any non-paracompact manifold with any non-empty manifold, the ball of...

In differential geometry, a hypercomplex manifold is a manifold with the tangent bundle equipped with an action by the algebra of quaternions in such a...

after Max Dehn, is a construction used to modify 3-manifolds. The process takes as input a 3-manifold together with a link. It is often conceptualized as...

In differential geometry, the holonomy of a connection on a smooth manifold is the extent to which parallel transport around closed loops fails to preserve...

Jack Thomas Manifold (born 14 August 2002) is an English YouTuber, live streamer and podcaster. He gained popularity for creating Minecraft videos and...

of the 4.4-litre V8 BMW S63 engine with the Cylinder-bank Comprehensive Manifold (CCM). The engine is rated 408 kW (547 hp) at 6,000 rpm and 677 N⋅m (499 lbf⋅ft)...

In mathematics, a piecewise linear manifold (PL manifold) is a topological manifold together with a piecewise linear structure on it. Such a structure...

particular instances of arithmetic groups. An arithmetic hyperbolic three-manifold is the quotient of hyperbolic space H 3 {\displaystyle \mathbb {H} ^{3}}...

complex manifolds. They were introduced by John Gray in 1959. Shigeo Sasaki in 1960 introduced Sasakian manifold to study them. Given a smooth manifold M {\displaystyle...

geometric structure on differentiable manifolds. It is a generalization of symplectic form. Given a differentiable manifold, a symplectic form over it is differential...

mathematical field of differential geometry, a Kenmotsu manifold is an almost-contact manifold endowed with a certain kind of Riemannian metric. They are...

In mathematics, a handle decomposition of an m-manifold M is a union ∅ = M − 1 ⊂ M 0 ⊂ M 1 ⊂ M 2 ⊂ ⋯ ⊂ M m − 1 ⊂ M m = M {\displaystyle \emptyset =M_{-1}\subset...

category of smooth manifolds. That is, E {\displaystyle E} , B {\displaystyle B} , and F {\displaystyle F} are required to be smooth manifolds and all the functions...

dealing with the topological properties and smooth properties of smooth manifolds. In this sense differential topology is distinct from the closely related...

based upon the flows generated by a smooth Hamiltonian over a symplectic manifold. The flows are symplectomorphisms and hence obey Liouville's theorem. This...

and is a type of Klein geometry. A conformal manifold is a Riemannian manifold (or pseudo-Riemannian manifold) equipped with an equivalence class of metric...

Dancer, Andrew S. (2000), "The geometry and topology of toric hyperkähler manifolds" (PDF), Communications in Analysis and Geometry, 8 (4): 727–760, doi:10...

mathematics, a submanifold of a manifold M {\displaystyle M} is a subset S {\displaystyle S} which itself has the structure of a manifold, and for which the inclusion...

10303-509 Manifold surface, a non intersecting area in 3D that is composed by advanced faces ISO 10303-521 Manifold subsurface, a sub-area out of a manifold surface...

classification of compact 3-manifolds. On a Kähler manifold, the Ricci curvature determines the first Chern class of the manifold (mod torsion). However,...

differential form of degree equal to the differentiable manifold dimension. Thus on a manifold M {\displaystyle M} of dimension n {\displaystyle n} , a...

politician and pastoralist James Chester Manifold and has remained closely associated with the prominent Manifold family. Designed by Colac architect Alexander...

the context of Sasakian manifold. If a contact manifold arises as a constant-energy hypersurface inside a symplectic manifold, then the Reeb vector field...

between geometric objects called Calabi–Yau manifolds. The term refers to a situation where two Calabi–Yau manifolds look very different geometrically but are...

In mathematics, the Weeks manifold, sometimes called the Fomenko–Matveev–Weeks manifold, is a closed hyperbolic 3-manifold obtained by (5, 2) and (5, 1)...

"Manifold Destiny" is an article in The New Yorker written by Sylvia Nasar and David Gruber and published in the 28 August 2006 issue of the magazine....

feature space or embedding space, is an embedding of a set of items within a manifold in which items resembling each other are positioned closer to one another...

In mathematics, a smooth compact manifold M is called almost flat if for any ε > 0 {\displaystyle \varepsilon >0} there is a Riemannian metric g ε {\displaystyle...

to express the curvature of Riemannian manifolds. It assigns a tensor to each point of a Riemannian manifold (i.e., it is a tensor field). It is a local...

A Seifert fiber space is a 3-manifold together with a decomposition as a disjoint union of circles. In other words, it is a S 1 {\displaystyle S^{1}} -bundle...

way of transporting geometrical data along smooth curves in a manifold. If the manifold is equipped with an affine connection (a covariant derivative...

the manifold; a manifold with a (positive-definite) metric is a Riemannian manifold, one with an indefinite metric is a pseudo-Riemannian manifold. Thus...

variable-length intake manifold (VLIM),variable intake manifold (VIM), or variable intake system (VIS) is an automobile internal combustion engine manifold technology...

between manifolds are studied, both as objects in their own right and for the light they shed. Just as there are various types of manifolds, there are...

mathematical physics. A smooth compact Riemannian manifold can be studied using analytic data. For a compact spin manifold M {\displaystyle M} , the algebra C ∞ (...

Mathematical Society for his "profoundly original" breakthrough article Three-manifolds with positive Ricci curvature, in which he first introduced and analyzed...

A (pseudo-)Riemannian manifold is conformally flat if each point has a neighborhood that can be mapped to flat space by a conformal transformation. In...

in differential topology, a Kervaire manifold K 4 n + 2 {\displaystyle K^{4n+2}} is a piecewise-linear manifold of dimension 4 n + 2 {\displaystyle 4n+2}...

space. Instead, the geometrization conjecture states that every closed 3-manifold can be decomposed in a canonical way into pieces that each have one of...

suitable alternative for such situations. Orientable manifolds with spinh structures are called spinh manifolds. H stands for the quaternions, which are denoted...

complex geometry is concerned with the study of spaces such as complex manifolds and complex algebraic varieties, functions of several complex variables...

components such as the throttle body-to-intake-manifold or upper-intake-manifold-to-lower-intake-manifold junctions. Requiring little more than longer fasteners...

3-manifolds. A manifold is prime if it is not homeomorphic to any connected sum of manifolds, except for the trivial connected sum of the manifold with...

may flow through one or more of the following: Cylinder head and exhaust manifold A turbocharger to increase engine power. A catalytic converter to reduce...

topology, capable of expressing basic topological information about smooth manifolds in a form particularly adapted to computation and the concrete representation...

Duvall in 1977. A manifold approximate fibration is a proper approximate fibration between manifolds. Some authors believe that manifold approximate fibrations...

microflexible sheaves, proving that they satisfy an h-principle on open manifolds.[G69] As a consequence (among other results) he was able to establish...

tangent vectors of a manifold. Alternatively, the covariant derivative is a way of introducing and working with a connection on a manifold by means of a differential...

strong Whitney embedding theorem states that any smooth real m-dimensional manifold (required also to be Hausdorff and second-countable) can be smoothly embedded...

manifolds called Ricci solitons. For a 3-dimensional manifold, Perelman showed how to continue past the singularities using surgery on the manifold....

quaternionic manifold is a quaternionic analog of a complex manifold. The definition is more complicated and technical than the one for complex manifolds due in...

Manifold Destiny is a 1989 cookbook (ISBN 0679723374), its updated 1998 edition (ISBN 0375751408) and a 2008 update (ISBN 1416596232) on the subject of...

class is a homology class [M] associated to a connected orientable compact manifold of dimension n, which corresponds to the generator of the homology group...

4-manifold is a special symmetric bilinear form on the 2nd (co)homology group of the 4-manifold. It reflects much of the topology of the 4-manifolds, including...

In mathematics, the category of manifolds, often denoted Manp, is the category whose objects are manifolds of smoothness class Cp and whose morphisms are...

Configuration space may refer to: Configuration space (physics) Configuration space (mathematics), the space of arrangements of points on a topological...

Park 10 miles north of Ashbourne, Derbyshire. A natural gateway to the Manifold Valley, the river crosses the road from Hartington (the nearest village)...

high-dimensional manifolds. Handles are used to particularly study 3-manifolds. Handlebodies play a similar role in the study of manifolds as simplicial...

consists of a tube, a one-way valve and a vacuum source (such as the inlet manifold). The unwanted gases, called blow-by, are gases from the combustion chamber...

cover of a Fano manifold is compact, and so can only be a finite covering. However, we have just seen that the Todd genus of a Fano manifold must equal 1...

Manifold: Origin (2001) is a science fiction novel by British author Stephen Baxter, the third instalment in the Manifold Trilogy. As with the other books...

any n-dimensional Riemannian manifold can be locally embedded in an (n + 1)-dimensional Ricci-flat Riemannian manifold. Campbell's theorem states that...

theorem or hyperbolization theorem implies that closed atoroidal Haken manifolds are hyperbolic, and in particular satisfy the Thurston conjecture. One...

Riemannian manifold is a smooth curve in the manifold that is not contained within any compact subset of the manifold. A complete manifold is one in which...

In topology, a surface is a two-dimensional manifold. Some surfaces arise as the boundaries of three-dimensional solid figures; for example, the sphere...

setting: G {\displaystyle G} is a Lie group, M {\displaystyle M} is a smooth manifold, and the action map is differentiable. Let σ : G × M → M , ( g , x ) ↦...

The study of manifolds combines many important areas of mathematics: it generalizes concepts such as curves and surfaces as well as ideas from linear...

The flow in manifolds is extensively encountered in many industrial processes when it is necessary to distribute a large fluid stream into several parallel...

describes a field Σ that takes on values in a nonlinear manifold called the target manifold  T. The non-linear σ-model was introduced by Gell-Mann &...

Swainsley Tunnel is a tunnel on the route of the former Leek and Manifold Light Railway, which connected the market town of Leek with Hulme End, via Waterhouses...

the Fubini–Study metric, such a manifold is always a Kähler manifold. By Chow's theorem, a projective complex manifold is also a smooth projective algebraic...

complex analysis, a Riemann surface is a connected one-dimensional complex manifold. These surfaces were first studied by and are named after Bernhard Riemann...

positive correlation matrices of mental test results (or the "positive manifold"), despite large differences in tests' contents, has been described as...

two) because, as a Riemannian manifold, distances are measured along geodesics within the manifold. In a Riemannian manifold whose Ricci curvature has a...

gas manifold) is a commonly used chemistry apparatus developed by Wilhelm Schlenk. It consists of a dual manifold with several ports. One manifold is connected...

for filling and connection to the regulator. Other accessories such as manifolds, cylinder bands, protective nets and boots and carrying handles may be...

In chemical kinetics, an intrinsic low-dimensional manifold is a technique to simplify the study of reaction mechanisms using dynamical systems, first...

is an isomorphism of differentiable manifolds. It is an invertible function that maps one differentiable manifold to another such that both the function...

the word "manifold" already has a different definition. I tried "foldamani", which was quickly displaced by the suggestion of "manifolded". After two...

manifolds out of disk bundles. It was first described by John Milnor (1956) and subsequently used extensively in surgery theory to produce manifolds and...

six-dimensional as the underlying manifold of the theory is three-dimensional as a complex manifold, hence six-dimensional as a real manifold. The theory has been...

mathematics, Rokhlin's theorem states that if a smooth, orientable, closed 4-manifold M has a spin structure (equivalently, if the second Stiefel–Whitney class...

configurations of the system is a manifold in the space of generalized coordinates. This manifold is called the configuration manifold of the system. Notice that...

invariant of (4k + 2)-dimensional manifolds (singly even-dimensional manifolds: surfaces (2-manifolds), 6-manifolds, 10-manifolds, etc.) with certain additional...

Riemannian flat manifold. Any hyperbolic 3-manifold is, by definition, covered by the hyperbolic 3-space H3, hence aspherical. As is any n-manifold whose universal...

Kähler manifold Ricci-flat manifold Calabi–Yau manifold Hyperkähler manifold K3 surface G2 manifold Spin(7)-manifold Generalized complex manifold Orbifold...

specifically differential geometry, the infinitesimal geometry of Riemannian manifolds with dimension greater than 2 is too complicated to be described by a...

Purrumbete near Camperdown, Victoria, Australia. Established in 1838 by the Manifold brothers, it is one of Victoria's oldest continuously occupied pastoral...

The data lie approximately on a manifold of much lower dimension than the input space. In this case learning the manifold using both the labeled and unlabeled...

Maclachlan, Colin; Reid, Alan W. (2003). The Arithmetic of Hyperbolic 3-Manifolds. Graduate Texts in Mathematics. Vol. 219. Springer-Verlag. ISBN 0-387-98386-4...

manifolds, and not every cone is homeomorphic to a manifold. Embedded representatives of 1-cycles, 3-cycles, and oriented 2-cycles all admit manifold-shaped...

include: a variable intake manifold, newly designed heads, and a larger drive by wire throttle chamber. The intake manifold directs air through different...

oriented manifolds of the same dimension is a number that represents the number of times that the domain manifold wraps around the range manifold under the...

In differential geometry, a G-structure on an n {\displaystyle n} -manifold M {\displaystyle M} , for a given structure group G {\displaystyle G} , is...

a generalized flag variety is a smooth or complex manifold, called a real or complex flag manifold. Flag varieties are naturally projective varieties...

definitions given below. Connection Curvature Metric space Riemannian manifold See also: Glossary of general topology Glossary of differential geometry...

The Leek and Manifold Valley Light Railway (L&MVLR) was a narrow gauge railway in Staffordshire, England, that operated between 1904 and 1934. The line...

different block. The European version used a "siamesed" two-port exhaust manifold, similar to the one used on the V4, while the American version used three-port...

village in the Staffordshire Peak District of England, lying on the River Manifold. The population of the civil parish as taken at the 2011 census was 402...

an n {\displaystyle \textstyle n} -dimensional manifold ⁠ M {\displaystyle M} ⁠, an integral manifold is an immersed (not necessarily embedded) submanifold...

states that a definite intersection form of a closed, oriented, smooth manifold of dimension 4 is diagonalizable. If the intersection form is positive...

to the top of the manifold so that they will be unobstructed when they are also pulled along. Yuasa successfully ascends the manifold, but Lemons' umbilical...

maps between such manifolds, similarly to how one defines smooth maps between smooth manifolds: if M and N are Lipschitz manifolds, then a function f...

algebraic varieties in a similar way as, for manifolds, charts are glued together for building a manifold. Like all affine varieties, local data on an...

flows. More specifically, the conjecture claims that on a compact contact manifold, its Reeb vector field should carry at least one periodic orbit. By definition...

field on a manifold is a formation of a line being tangent to a manifold at each point, i.e. a section of the line bundle over the manifold. Line fields...

geometrical theory of gravitation are tensor fields defined on a Lorentzian manifold representing spacetime. This article is a general description of the mathematics...

differentiable manifold is an invariant which encodes the stable normal (dually, tangential) data. There are analogs for generalizations of manifold, notably...

formed by the stable manifold and unstable manifold of a fixed point. Let f : M → M {\displaystyle f:M\to M} be a map defined on a manifold M {\displaystyle...

of a compact Riemannian manifold with negative Ricci curvature must be zero. Consequently the isometry group of the manifold must be finite. The theorem...

Riemannian or pseudo-Riemannian manifold induced by its metric tensor. There are similar isomorphisms on symplectic manifolds. These isomorphisms are global...

(1963), states that for an elliptic differential operator on a compact manifold, the analytical index (related to the dimension of the space of solutions)...

theory models gravitation as the curvature of a four dimensional Lorentzian manifold (a spacetime) and the concepts of topology thus become important in analysing...

In oil and gas production a choke manifold is used to lower the pressure from the well head. It consist of a set of high pressure valves and at least two...

the Courant Institute in New York University, where he began work on manifolds with lower bounds on Ricci curvature. From there, he accepted a two-year...

of the curvature of spacetime or, more generally, a pseudo-Riemannian manifold. Like the Riemann curvature tensor, the Weyl tensor expresses the tidal...

one-piece cast crankshaft, iron-coated aluminum pistons and a magnesium intake manifold. Like the M112, a balance shaft is installed in the engine block between...

"turbo-normalized" systems. Generally, a turbo-normalized system attempts to maintain a manifold pressure of 29.5 inHg (100 kPa). The most commonly used forced-induction...

from air manifolds equipped with quick-disconnect fittings. These air manifolds are located throughout the submarine. While connected to a manifold, the wearer...

a complex differential form is a differential form on a manifold (usually a complex manifold) which is permitted to have complex coefficients. Complex...

the shortest non-contractible loop on a Riemannian manifold in terms of the volume of the manifold. Gromov's systolic inequality was proved in 1983; it...

geometrization conjecture Hyperbolic 3-manifolds Spherical 3-manifolds Euclidean 3-manifolds, Bieberbach Theorem, Flat manifolds, Crystallographic groups Seifert...

prototypical example of a Riemann surface, and is one of the simplest complex manifolds. In projective geometry, the sphere is an example of a complex projective...

Poisson structure on a manifold M {\displaystyle M} , then its graph is a (closed) Dirac structure. Any submanifold of a Poisson manifold induces a Dirac structure...

vacua for the quantum field theory is a manifold (or orbifold), usually called the vacuum manifold. This manifold is often called the moduli space of vacua...

Chern's conjecture for affinely flat manifolds was proposed by Shiing-Shen Chern in 1955 in the field of affine geometry. As of 2025, it remains an unsolved...

theorem, named after Georges Reeb, states that A closed oriented connected manifold M n that admits a singular foliation having only centers is homeomorphic...

Calculus on manifolds may refer to: Calculus on Manifolds, an undergraduate real analysis and differential geometry textbook by Michael Spivak The generalization...

information geometry the corresponding statistical manifold is interpreted as a (dually) flat manifold. This allows many techniques of optimization theory...

innate restriction in the engine's inlet tract, which includes the intake manifold, a small pressure drop occurs as air is drawn in, resulting in a volumetric...

sometimes solder form) of a fiber bundle to a smooth manifold is a manner of attaching the fibers to the manifold in such a way that they can be regarded as tangent...

exhaust system (manifold or header assembly and associated clamps susceptible to rust, corrosion or fatigue such as the exhaust manifold splintering after...

In mathematics, a p-dimensional foliation is a partition of a manifold into submanifolds, all of the same dimension p, locally modeled on the decomposition...

{\displaystyle X} (for example X {\displaystyle X} could be a topological space, a manifold, or an algebraic variety): to every point x {\displaystyle x} of the space...

tip. A glowplug system consists of either a single glowplug in the inlet manifold, or one glowplug per cylinder. In older systems, the driver is required...

In mathematics, a smooth structure on a manifold allows for an unambiguous notion of smooth function. In particular, a smooth structure allows mathematical...

of connected sum is a geometric modification on manifolds. Its effect is to join two given manifolds together near a chosen point on each. This construction...

atmosphere or by recirculating air back ("diverting") into the intake manifold. Thus, a recirculating blowoff valve that recycles pressurized air back...

curvature Kähler metric (cscK metric) is a Kähler metric on a complex manifold whose scalar curvature is constant. A special case is a Kähler–Einstein...

mathematics called differential topology, an exotic sphere is a differentiable manifold M that is homeomorphic but not diffeomorphic to the standard Euclidean...

often refers to a specific class of 3-manifolds, but in general can be defined for higher dimensions. In the 3-manifold case, a lens space can be visualized...

on a (usually, but not necessarily, two-dimensional) compact Riemannian manifold (M, g) such that every geodesic through x also passes through y, and the...

the world's first engine to use a continuously variable-length intake manifold, and BMW's first V8 to feature variable valve lift (called Valvetronic)...

Using four-dimensional Cerf theory, he proved that if M and N are 3-manifolds, resulting from Dehn surgery on framed links L and J respectively, then...

> 1 {\displaystyle m>1} , any smooth m {\displaystyle m} -dimensional manifold (required also to be Hausdorff and second-countable) has a one-to-one immersion...

compact complex tori, K3 surfaces are the Calabi–Yau manifolds (and also the hyperkähler manifolds) of dimension two. As such, they are at the center of...

Manifold is an unincorporated community and coal town in Washington County, Pennsylvania, United States. U.S. Geological Survey Geographic Names Information...

lightweight construction: reduced wall thickness and steel sheet exhaust manifold (instead of cast-iron), one near-engine-mounted catalytic pre-converter...

curved compact Riemannian manifold. It is named for Alexandre Preissmann, who published a proof in 1943. Consider a closed manifold with a Riemannian metric...

theory defined for any smooth manifold. It is constructed using the smooth structure and an auxiliary metric on the manifold, but turns out to be topologically...

groups of manifolds; and in particular with the limitations on topological groups G that can act effectively (faithfully) on a (topological) manifold M. Restricting...

geometry, a metric tensor (or simply metric) is an additional structure on a manifold M (such as a surface) that allows defining distances and angles, just as...

casing. The cylinder-head circuit heats the cabin's interior. The exhaust manifold is integrated into the cylinder head, enabling the engine to warm up more...

that has been decomposed into pieces called strata; these strata are manifolds and are required to fit together in a certain way. Thom–Mather stratified...

sheaves on one Calabi–Yau manifold is equivalent in a certain sense to the Fukaya category of a completely different Calabi–Yau manifold. This equivalence provides...

Poincaré conjecture. Freedman and Robion Kirby showed that an exotic R4 manifold exists. Freedman was born in Los Angeles, California, in the United States...

replacing a triangulation of a piecewise linear manifold by a different triangulation of a homeomorphic manifold. Pachner moves are also called bistellar flips...

In mathematics, it has been used to calculate knot invariants and three-manifold invariants such as the Jones polynomial. Particularly, Chern–Simons theory...

Major-General Sir William Digby Manifold Raeburn, KCVO, CB, DSO, MBE (1915–2001) was a senior British Army officer. He was Resident Governor of the Tower...

conjecture is a statement that a manifold that is a homotopy sphere is a sphere. More precisely, one fixes a category of manifolds: topological (Top), piecewise...

fitted to both camshafts (called "double-VANOS"), a dual length intake manifold (called "DISA") is used and the thermostat is electronically controlled...

of dimension n is the unique simply connected, n-dimensional Riemannian manifold of constant negative sectional curvature, often taken to be  −1 for simplicity...

mathematics, a complex torus is a particular kind of complex manifold M whose underlying smooth manifold is a torus in the usual sense (i.e. the cartesian product...

one of the two manifolds is a "comparison model", generally a manifold with constant curvature, and the second one is the manifold under study : a bound...

scalar) is a measure of the curvature of a Riemannian manifold. To each point on a Riemannian manifold, it assigns a single real number determined by the...

of multivariable calculus topics Manifold Differentiable manifold Smooth manifold Banach manifold Fréchet manifold Tensor analysis Tangent vector Tangent...

the Dold–Thom theorem, the Dold–Kan correspondence, and introduced Dold manifolds, Dold–Puppe stabilization, and Dold fibrations. Albrecht Dold was born...

embedding (or immersion). Let ( M , g ) {\displaystyle (M,g)} be a Riemannian manifold, and S ⊂ M {\displaystyle S\subset M} a Riemannian submanifold. Define...

Higher output versions of the N52 use a three-stage variable length intake manifold (also called "DISA"). The N52 engine block is made from a combination of...

Women aged 18 to 34 had sex less often as well. Reasons for this trend are manifold. People who were unemployed, only had part-time jobs, and students were...

a G2 manifold if one wishes to recover the physics of our four-dimensional world. Another problem is that G2 manifolds are not complex manifolds, so theorists...

piston controls the exhaust port. In a four-stroke engine, an exhaust manifold which is designed to maximise the power output of an engine is often called...

Riemannian manifold with positive sectional curvature has positive Euler characteristic. A compact, (2d)-dimensional Riemannian manifold with negative...

cubic graph, this complex always forms a manifold. The graph is said to be circularly embedded onto the manifold, in that every face of the embedding is...

concerning 3-manifolds revolve around normal surface theory, which is a phrase that encompasses several techniques to turn problems in 3-manifold theory into...

smooth manifold which connects nearby tangent spaces, so it permits tangent vector fields to be differentiated as if they were functions on the manifold with...

from the manifold when closed, and the manifold can be attached or disconnected while the cylinders are pressurised. More recently, manifolds have become...

circle and whose fiber is the original space X. If X is a manifold, Mf will be a manifold of dimension one higher, and it is said to "fiber over the...

sensor coolant temperature sensor crankshaft position sensor knock sensors manifold absolute pressure sensor (MAP sensor) intake air temperature sensor intake...

systems can be highly complex, and often include specially designed intake manifolds to optimally distribute air and air/fuel mixture to each cylinder. Many...

Streets, and Roslyn Road. On 21 October 1910, chairman of the school, W. T. Manifold turned the first sod at the site of what was expected to be a new era for...

In mathematics, an Eells–Kuiper manifold is a compactification of R n {\displaystyle \mathbb {R} ^{n}} by a sphere of dimension n / 2 {\displaystyle n/2}...

In mathematics, a connected submanifold of a compact manifold with boundary is said to be boundary parallel, ∂-parallel, or peripheral if it can be continuously...

complexity of a manifold. More generally, the simplicial norm measures the complexity of homology classes. Given a closed and oriented manifold, one defines...

having no sources or sinks. Let M {\displaystyle M} be a differentiable manifold, of dimension n {\displaystyle n} , and v {\displaystyle v} a vector field...

polynomials. As v {\displaystyle v} passes through each of these values, a manifold containing all states with that value of N {\displaystyle N} arises at...

point of a region of a mathematical space (typically a Euclidean space or manifold) or of a physical space, in which case the field quantity acquires a unit...

probabilities for these), or a manifold (e.g. the state of a black hole can be described by a metric tensor on a Riemann manifold and its position will be a...

more specifically in manifold theory, projective spaces play a fundamental role, being typical examples of non-orientable manifolds. As outlined above,...

proximity to the urinary and gastrointestinal tracts. Specific causes are manifold and include obstructed labor, hysterectomy, malignancy, radiation, episiotomy...

Euclidean space and, even more generally, on Riemannian and pseudo-Riemannian manifolds. It is named after Pierre-Simon Laplace and Eugenio Beltrami. For any...

Regina is a suite of mathematical software for 3-manifold topologists. It focuses upon the study of 3-manifold triangulations and includes support for normal...

concepts of hyperplane, plane curve, and surface. A hypersurface is a manifold or an algebraic variety of dimension n − 1, which is embedded in an ambient...

the two notions ANR and local ANR coincide. In particular, a topological manifold is an ANR (even strongly it is a Euclidean neighborhood retract.) There...

mathematician William Thurston in his influential 1982 paper Three-dimensional manifolds, Kleinian groups and hyperbolic geometry published in the Bulletin of...

upgrade for the M52 is to swap the inlet manifold for the more free-flowing runners found on the M50 inlet manifold. As the blocks and head are essentially...

the n-torus is a solvmanifold. For n = 2 {\displaystyle n=2} , these manifolds belong to Sol, one of the eight Thurston geometries. A solvmanifold is...

connection, gives a means for parallel transport of tangent vectors on a manifold from one point to another along a curve. An affine connection is typically...

clamp and bracket Exhaust flange gasket Exhaust gasket Exhaust manifold Exhaust manifold gasket Exhaust pipe Heat shield Heat sleeving and tape Resonator...

James Chester Manifold (10 February 1867 – 30 October 1918) was an Australian politician and philanthropist. Manifold was born at Purrumbete, near Camperdown...

compact 3-manifold; the boundary of XK and the boundary of the neighborhood N are homeomorphic to a two-torus. Sometimes the ambient manifold M is understood...

statement about the scalar curvature of Riemannian manifolds: Let (M,g) be a closed smooth Riemannian manifold. Then there exists a positive and smooth function...

Riemannian metric which can be defined on a smooth statistical manifold, i.e., a smooth manifold whose points are probability distributions. It can be used...

(or differentiable) manifold M {\displaystyle {\mathcal {M}}} ; one can define a cotangent space for every point on a smooth manifold. Typically, the cotangent...

the performance of his 1932 Ford Roadster led him to design a new intake manifold. Friends and fellow drivers soon wanted one as well. This transformed his...

configuration space manifold Q, so that the rank of the cometric is less than the dimension of the manifold Q, one has a sub-Riemannian manifold. The Hamiltonian...

quadratic form is defined for a smooth immersed submanifold in a Riemannian manifold. The second fundamental form of a parametric surface S in R3 was introduced...

connection is the unique affine connection on the tangent bundle of a manifold that preserves the (pseudo-)Riemannian metric and is torsion-free. The...

On a differentiable manifold, the exterior derivative extends the concept of the differential of a function to differential forms of higher degree. The...

the homology and cohomology groups of manifolds. It states that if M is an n-dimensional oriented closed manifold (compact and without boundary), then...

directly into the combustion chamber, unlike manifold injection systems, which inject fuel into the intake manifold so that it mixes with the incoming airstream...

the complex numbers, amongst compact Kähler manifolds. In effect it says precisely which complex manifolds are defined by homogeneous polynomials. Kunihiko...

smooth manifolds via de Rham cohomology, or Čech or sheaf cohomology to investigate the solvability of differential equations defined on the manifold in question...

an important class of functions used in complex analysis. On a Kähler manifold, plurisubharmonic functions form a subset of the subharmonic functions...

geometry, Hironaka's example is a non-Kähler complex manifold that is a deformation of Kähler manifolds found by Heisuke Hironaka (1960, 1962). Hironaka's...

In Riemannian geometry, the unit tangent bundle of a Riemannian manifold (M, g), denoted by T1M, UT(M), UTM, or SM is the unit sphere bundle for the tangent...

geometrically finite if it has a well-behaved fundamental domain. A hyperbolic manifold is called geometrically finite if it can be described in terms of geometrically...

the form of a Calabi–Yau manifold. Within the more complete framework of M-theory, they would have to take form of a G2 manifold. A particular exact symmetry...

Flamelet-Generated Manifold (FGM) is a combustion chemistry reduction technique[dubious – discuss]. The approach of FGM is based on the idea that the most...

study of quantum groups. Manifolds with a Poisson algebra structure are known as Poisson manifolds, of which the symplectic manifolds and the Poisson–Lie groups...

turbocharger pressurises the intake air before it enters the inlet (intake) manifold. In the case of a turbocharger, the compressor is powered by the kinetic...

In mathematics, a handle decomposition of a 3-manifold allows simplification of the original 3-manifold into pieces which are easier to study. An important...

station wagons. It featured a 4-barrel carburetor and matching intake manifold, chrome unsilenced air cleaner with callout sticker, longer-duration and...

induced on the corresponding bundle (e.g., the geodesic spray on Finsler manifolds.) Since the early 1980s, jet bundles have appeared as a concise way to...

the intrinsic geometry of a data manifold based on a rough estimate of each data point’s neighbors on the manifold. Isomap is highly efficient and generally...

with a different definition used in algebraic topology and the theory of manifolds. Despite widespread acceptance of the meaning of the terms boundary and...

pseudo-Riemannian manifold can be given as a metric product. The best-known is the Cheeger–Gromoll splitting theorem for Riemannian manifolds, although there...

standardize the position of the points or other geometric elements on a manifold such as Euclidean space. The coordinates are not interchangeable; they...

not a manifold, it is a generalized homological manifold and a homotopy manifold. List of topologies Whitehead manifold, a contractible 3-manifold not homeomorphic...

mathematical field of differential geometry, a calibrated manifold is a Riemannian manifold (M,g) of dimension n equipped with a differential p-form φ...

In what follows, manifolds are understood to be without boundary, unless stated otherwise. A closed manifold means a compact manifold (without boundary)...

mathematics, an immersion is a differentiable function between differentiable manifolds whose differential pushforward is everywhere injective. Explicitly, f :...

probability theory and statistics. It studies statistical manifolds, which are Riemannian manifolds whose points correspond to probability distributions....

necessitated a redesigned exhaust manifold arrangement; originally this took the form of a one-piece eight into one Monel manifold that re-routed the exhaust...

were jointly developed by the GEMA companies, but the intake and exhaust manifolds, the cylinder head's intake and exhaust ports, and other elements related...

dimension of a manifold or an algebraic variety. When degrees of freedom is used instead of dimension, this usually means that the manifold or variety that...

bitensor (or bi-tensor) is a tensorial object that depends on two points in a manifold, as opposed to ordinary tensors which depend on a single point. Bitensors...

of a 2 n c {\displaystyle 2n_{c}} -dimensional manifold, known as the scalar manifold. This manifold can be parametrized using complex coordinates (...

naturally aspirated, with variable-length intake manifold via butterfly valve in intake manifold Intake manifold: carbon fibre reinforced polymer Block: nodular...

either electric fuel pumps mounted inside the fuel tank (for lower pressure manifold injection systems) or high-pressure mechanical pumps mounted on the engine...

embedded in the data space. This system approximates a low-dimensional manifold. The elastic coefficients of this system allow the switch from completely...

to Manifolds is a mathematics textbook written by Loring W. Tu providing an introduction to differential and integral calculus on smooth manifolds. It...

fuel economy inevitably resulted. By 1973, an EGR valve controlled by manifold vacuum opened or closed to admit exhaust to the intake tract only under...

a homoclinic orbit lies in the intersection of the stable manifold and the unstable manifold of an equilibrium. It is a heteroclinic orbit–a path between...

being homotopy equivalent to a closed manifold. Normal maps also apply to the study of the uniqueness of manifold structures within a homotopy type, which...

Jetronic is a trade name of a manifold injection technology for automotive petrol engines, developed and marketed by Robert Bosch GmbH from the 1960s onwards...

four-dimensional spacetime; it can be any (pseudo-)Riemannian manifold, or even a supersymmetric manifold or orbifold or even a noncommutative space. The construction...

tool associated with a Hamiltonian action of a Lie group on a symplectic manifold, used to construct conserved quantities for the action. The momentum map...

uses a reinforced plastic intake manifold (although a few of the 1995 and 1996 engines received an aluminum intake manifold due to a shortage of the plastic...

the scalar manifold, which is the field space manifold whose coordinates are the scalars. Global supersymmetry implies that this manifold must be a special...

In mathematics and physics, a Hamiltonian vector field on a symplectic manifold is a vector field defined for any energy function or Hamiltonian. Named...

University Press, ISBN 978-0-521-61558-7, MR 0903850 Thurston, William (1980), The geometry and topology of three-manifolds, Princeton lecture notes v t e...

offloading gas or liquid products. SPMs are the link between geostatic subsea manifold connections and weathervaning tankers. They are capable of handling any...

being related to, among other things, knot theory, the theory of four-manifolds, and algebraic topology, and to the theory of moduli spaces in algebraic...

one-piece cast camshafts, a timing chain, and a cast aluminium lower intake manifold. Some variants use multi-port fuel injection, some have D4 direct injection...

topological theory based on the concept of the boundary of a manifold. For context see timeline of manifolds. Jean Dieudonné wrote that cobordism returns to the...

-vector field, on a smooth manifold M {\displaystyle M} , is a generalization of the notion of a vector field on a manifold. A multivector field of degree...

certain condition on the causal structure of a spacetime manifold (that is, a Lorentzian manifold). It is called hyperbolic in analogy with the linear theory...

cone is a generalization of the notion of the tangent space (applied to manifolds in the usual differential geometry setting) to irregular surfaces, that...

Manifold Data Mining Inc. is a Canadian company specializing in consumer data products, analytics, and predictive modeling. As a data and analytical service...

no matter how bad the small subspace is. The Whitehead manifold is an example of a 3-manifold that is contractible but not simply connected at infinity...

Phase Space (subtitled Stories from the Manifold and Elsewhere) is a 2003 science fiction collection by British writer Stephen Baxter, containing twenty-three...

smaller space (e.g., 2D). The manifold hypothesis proposes that high-dimensional data sets lie along low-dimensional manifolds, and many dimensionality reduction...

important type of G-structure that can be defined on a smooth manifold. If M is a smooth manifold of dimension seven, then a G2-structure is a reduction of...

arithmetic geometry, the Mazur swindle in geometric topology, and the Mazur manifold in differential topology. Born in New York City, Mazur attended the Bronx...

classification of closed orientable Riemannian 2-manifolds into elliptic/parabolic/hyperbolic cases. Each such manifold has a conformally equivalent Riemannian...

for a differentiable manifold M is a set of basis vector fields {e1, ..., en} defined at every point P of a region of the manifold as e α = lim δ x α →...

X} is a manifold, its ordered configuration spaces are open subspaces of the powers of X {\displaystyle X} and are thus themselves manifolds. The configuration...

says is equally applicable to (pseudo-)Riemannian manifolds in general, and even to spin manifolds. Most statements hold by substituting arbitrary n {\displaystyle...

opened jointly by the North Staffordshire Railway (NSR) and the Leek and Manifold Valley Light Railway (L&MVLR) in 1905 and closed in 1943. The station was...

constructing new invariants of smooth manifolds, the construction of exotic geometric structures such as hyperkähler manifolds, as well as giving alternative...

are indicative of the center manifold's existence. Likewise, the eigenvectors of the Jacobian reveal the center manifold's orientation. The Hodgkin–Huxley...

In the mathematical field of topology, a manifold M is called topologically rigid if every manifold homotopically equivalent to M is also homeomorphic...

rolled crankshaft, sinter forged connecting rods, a variable-length intake manifold, twin knock control sensors and coil-on-plug ignition. It was developed...

manifolds of the same dimension are locally symplectomorphic to one another. That is, every 2 n {\displaystyle 2n} -dimensional symplectic manifold can...

a Riemannian manifold to its topology. It is named for John Lighton Synge, who proved it in 1936. Let M be a closed Riemannian manifold with positive...

on a set generalizes the concept of a smooth atlas of a differentiable manifold, by declaring only what constitutes the "smooth parametrizations" into...

intake manifold, or housed in the throttle body. In a carbureted engine, it is found in the carburetor. When a throttle is wide open, the intake manifold is...

aircraft with constant-speed propellers also use inches of mercury to measure manifold pressure, which is indicative of engine power produced in engines equipped...

used the E8 lattice to construct an example of a topological 4-manifold, the E8 manifold, which has no smooth structure. Antony Garrett Lisi's incomplete...

his work on the topology of smooth (differentiable) four-dimensional manifolds, Donaldson–Thomas theory, and his contributions to Kähler geometry. He...

SK096584). It is on the Manifold Way, an 8-mile (13 km) walk and cycle path that follows the line of the former Leek and Manifold Valley Light Railway....

Forms and Geometric Invariants," from which the theory arose. Given a manifold and a Lie algebra valued 1-form A {\displaystyle \mathbf {A} } over it...

hyperbolic fixed point is a fixed point that does not have any center manifolds. Near a hyperbolic point the orbits of a two-dimensional, non-dissipative...

-dimensional manifold that measures whether the manifold could be surgically converted into a sphere. This invariant evaluates to 0 if the manifold can be converted...

abstract 20th century definition of coordinates on the cotangent bundle of a manifold (the mathematical notion of phase space). In classical mechanics, canonical...

In mathematics, given an exterior differential system defined on a manifold M, the Cartan–Kuranishi prolongation theorem says that after a finite number...

connection is a specialization of the affine connection to surfaces or other manifolds endowed with a metric, allowing distances to be measured on that surface...

In algebraic topology, a homology sphere is an n-manifold X having the homology groups of an n-sphere, for some integer n ≥ 1 {\displaystyle n\geq 1} ...

vacuum lines. The upper intake manifold then bolts to the lower section and is unlike the EA82 or EJ22 "spider" manifold designs in that there is no central...

thereby advancing the ignition timing. Vacuum advance typically uses manifold vacuum to adjust the ignition timing, for example to improve fuel economy...

parallelization of a manifold M {\displaystyle M\,} of dimension n is a set of n global smooth linearly independent vector fields. Given a manifold M {\displaystyle...

theorem of Riemannian geometry that largely reduces the study of complete manifolds of non-negative sectional curvature to that of the compact case. Jeff...

mixture escapes through the exhaust valves and combusts in the hot exhaust manifold, spooling the turbocharger and creating higher usable pressure. ALSes were...

bound on the volume of a Riemannian manifold and also gives a necessary and sufficient condition for the manifold to be isometric to the m-dimensional...

formally, it is an example of a non-orientable surface, a two-dimensional manifold on which one cannot define a consistent direction perpendicular to the...

symplectic toric manifolds in term of a special class of polytopes. It was proved by Thomas Delzant in 1988. A symplectic toric manifold is a compact connected...

smooth manifold are defined to be the Pontryagin classes of its tangent bundle. Novikov proved in 1966 that if two compact, oriented, smooth manifolds are...

studies the topology of a complex manifold by looking at the critical points of a holomorphic function on the manifold. It was introduced by Émile Picard...

The Geometry of Four-Manifolds is a mathematical textbook about Yang–Mills theory, or more generally gauge theory, and its application to the study of...

differential geometry and dynamical systems, a closed geodesic on a Riemannian manifold is a geodesic that returns to its starting point with the same tangent...

4-manifolds, and showed that they were more subtle than smooth manifolds in any other dimension, and also quite different from topological 4-manifolds....

and a magnesium intake manifold. The cylinders are lined with silicon/aluminium, and a dual-length variable-length intake manifold is fitted. In addition...

parameter space for which the system is critical is called a critical manifold. As an example consider a substance ferromagnetic below a transition temperature...

Riemannian manifold, is a harmonic map if and only if it is a geodesic. If ⁠ M {\displaystyle M} ⁠ and ⁠ N {\displaystyle N} ⁠ are two Riemannian manifolds, then...

pseudomanifold is a special type of topological space. It looks like a manifold at most of its points, but it may contain singularities. For example, the...

for intake and exhaust manifolds with runners of longer and more nearly equal length compared to the rake- or log-style manifolds typical of other inline...

Hamps is a river in Staffordshire, England. It is a tributary of the River Manifold, which itself flows into the River Dove near Ilam. For much of its length...

counterexample is the long line, which is a nonparacompact topological manifold. (The long line is locally compact, but not second countable.) Another...